15edo: Difference between revisions

Line 472:

In these notations, the nominals form a circle of perfect fifths. The other notes are notated using accidentals that raise or lower by one edostep.

==== ~~Ups~~ and downs notation (heptatonic) ====

==== Stein–Zimmermann–Gould notation (heptatonic) ====

15edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that downsharp is equivalent to dup (double-up) and upflat is equivalent to dud (double-down).{{Sharpness-sharp3a}}[[~~Alternative symbols~~ for ~~ups and downs~~ notation]] ~~uses sharps~~ and ~~flats with arrows, borrowed from extended~~ [[~~Helmholtz–Ellis~~ notation]]:{{~~Sharpness-sharp3~~}}

[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:

==== Kite's ups and downs notation (heptatonic) ====

15edo can be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that downsharp is equivalent to dup (double-up) and upflat is equivalent to dud (double-down).

==== Sagittal notation (heptatonic) ====

This notation uses the same sagittal sequence as edos [[22edo #Sagittal notation|22]] and [[29edo #Sagittal notation|29]], is a subset of the notation for [[30edo #Sagittal notation|30edo]], and is a superset of the notation for [[5edo #Sagittal notation|5edo]].

==== "Eef" notation (pentatonic) ====

[[Kite Giedraitis]] proposes pentatonic (as opposed to heptatonic) note names that omit B and merge E and F into a new letter "eef" that rhymes with "leaf". Eef, like E, is a 5th above A. Eef, like F, is a 4th above C. Eef is written like an E, but with the bottom horizontal line going not right but left from the vertical line. Eef can be typed as ꘙ (unicode A619) or ⊧ (unicode 22A7) or 𐐆 (unicode 10406). The circle of 5ths is C G D A ꘙ C. All intervals are either perfect, upperfect or downperfect (never major or minor). This is similar to heptatonic interval names in 7edo, 14edo, 21edo, etc.

{| class="wikitable"

|C

| C || ^C || vD || D || ^D || vꘙ || ꘙ || ^ꘙ || vG || G || ^G || vA || A || ^A || vC || C

|^C

|vD

|D

|^D

|vꘙ

|ꘙ

|^ꘙ

|vG

|G

|^G

|vA

|A

|^A

|vC

|C

|-

|P1

| P1 || ^1 || v2 || P2 || ^2 || v3 || P3 || ^3 || v4 || P4 || ^4 || v5 || P5 || ^5 || v6 || P6

|^1

|v2

|P2

|^2

|v3

|P3

|^3

|v4

|P4

|^4

|v5

|P5

|^5

|v6

|P6

|}

~~==== Sagittal notation (heptatonic)====~~

This notation uses the same sagittal sequence as EDOs [[22edo#Sagittal notation|22]] and [[29edo#Sagittal notation|29]], is a subset of the notation for [[30edo#Sagittal notation|30-EDO]], and is a superset of the notation for [[5edo#Sagittal notation|5-EDO]].

~~{{Sagittal chart|}}~~

==== Blackwood guitar notation ====

On a 15edo guitar, because the "perfect fourth" comes from 5edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the [[circle of fourths]] on ~~B — B-E-A-D-G~~-(B) ~~— then~~ the open strings of the guitar can be notated as usual (~~E-A-D-G-B-E~~). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15edo, it is necessary to use accidentals to notate intervals on the other two chains of 5edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15edo on the guitar, since 5edo provides a useful set of 3-limit landmarks (or "perfect fourths" and "perfect fifths") that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.

On a 15edo guitar, because the "perfect fourth" comes from 5edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the [[circle of fourths]] on B—B–E–A–D–G-(B)—then the open strings of the guitar can be notated as usual (E–A–D–G–B–E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15edo, it is necessary to use accidentals to notate intervals on the other two chains of 5edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15edo on the guitar, since 5edo provides a useful set of 3-limit landmarks (or "perfect fourths" and "perfect fifths") that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.

=== Blackwood decatonic notation ===

@@ Line 472: / Line 472: @@
 In these notations, the nominals form a circle of perfect fifths. The other notes are notated using accidentals that raise or lower by one edostep.
-==== Ups and downs notation (heptatonic) ====
+==== Stein–Zimmermann–Gould notation (heptatonic) ====
-edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that downsharp is equivalent to dup (double-up) and upflat is equivalent to dud (double-down).{{Sharpness-sharp3a}}[[Alternative symbols for ups and downs notation]] uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:{{Sharpness-sharp3}}
+[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
+{{Sharpness-sharp3-szg}}
+==== Kite's ups and downs notation (heptatonic) ====
+edo can be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that downsharp is equivalent to dup (double-up) and upflat is equivalent to dud (double-down).
+{{Sharpness-sharp3a}}
+==== Sagittal notation (heptatonic) ====
+This notation uses the same sagittal sequence as edos [[22edo #Sagittal notation|22]] and [[29edo #Sagittal notation|29]], is a subset of the notation for [[30edo #Sagittal notation|30edo]], and is a superset of the notation for [[5edo #Sagittal notation|5edo]].
+{{Sagittal chart|}}
 ==== "Eef" notation (pentatonic) ====
 [[Kite Giedraitis]] proposes pentatonic (as opposed to heptatonic) note names that omit B and merge E and F into a new letter "eef" that rhymes with "leaf". Eef, like E, is a 5th above A. Eef, like F, is a 4th above C. Eef is written like an E, but with the bottom horizontal line going not right but left from the vertical line. Eef can be typed as ꘙ (unicode A619) or ⊧ (unicode 22A7) or 𐐆 (unicode 10406). The circle of 5ths is C G D A ꘙ C. All intervals are either perfect, upperfect or downperfect (never major or minor). This is similar to heptatonic interval names in 7edo, 14edo, 21edo, etc.
 {| class="wikitable"
-|C
+| C || ^C || vD || D || ^D || vꘙ || ꘙ || ^ꘙ || vG || G || ^G || vA || A || ^A || vC || C
-|^C
-|vD
-|D
-|^D
-|vꘙ
-|ꘙ
-|^ꘙ
-|vG
-|G
-|^G
-|vA
-|A
-|^A
-|vC
-|C
 |-
-|P1
+| P1 || ^1 || v2 || P2 || ^2 || v3 || P3 || ^3 || v4 || P4 || ^4 || v5 || P5 || ^5 || v6 || P6
-|^1
-|v2
-|P2
-|^2
-|v3
-|P3
-|^3
-|v4
-|P4
-|^4
-|v5
-|P5
-|^5
-|v6
-|P6
 |}
-==== Sagittal notation (heptatonic)====
-This notation uses the same sagittal sequence as EDOs [[22edo#Sagittal notation|22]] and [[29edo#Sagittal notation|29]], is a subset of the notation for [[30edo#Sagittal notation|30-EDO]], and is a superset of the notation for [[5edo#Sagittal notation|5-EDO]].
-{{Sagittal chart|}}
 ==== Blackwood guitar notation ====
-On a 15edo guitar, because the "perfect fourth" comes from 5edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the [[circle of fourths]] on B — B-E-A-D-G-(B) — then the open strings of the guitar can be notated as usual (E-A-D-G-B-E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15edo, it is necessary to use accidentals to notate intervals on the other two chains of 5edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15edo on the guitar, since 5edo provides a useful set of 3-limit landmarks (or "perfect fourths" and "perfect fifths") that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.
+On a 15edo guitar, because the "perfect fourth" comes from 5edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the [[circle of fourths]] on B—B–E–A–D–G-(B)—then the open strings of the guitar can be notated as usual (E–A–D–G–B–E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15edo, it is necessary to use accidentals to notate intervals on the other two chains of 5edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15edo on the guitar, since 5edo provides a useful set of 3-limit landmarks (or "perfect fourths" and "perfect fifths") that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.
 === Blackwood decatonic notation ===